Download UNIVERSITY OF CALICUT 2014 Admission onwards III Semester STATISTICAL INFERENCE

Sampling Distribution
1
UNIVERSITY OF CALICUT
SCHOOL OF DISTANCE EDUCATION
BSc. MATHEMATICS
COMPLEMENTARY COURSE
CUCBCSS
2014 Admission onwards
III Semester
STATISTICAL INFERENCE
Question Bank
1.
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4.
The number of possible samples of size n out of N population units
with replacement is
a. N2
b. n2 c.  d. N!
Simple random sample can be drawn with the help of
a. random number tables b. Chit method
c. roulette wheel
d. all the above
Which of following statement is true
a. more the SE, better it is
b. less the SE, better it is
c. SE in always zero
d. SE is always unity
If the samples values are 1, 3, 5, 6, 9, the SE of the sample mean is
a. SE =
5.
2
b. SE = 1/
2
c. SE = 2.0 d. SE = 1/2
Student’s ‘t’ distribution was discovered by
a. G.W. Snedecor b. R.A. Fisher
c. W.Z. Gosset
c. Karl Pearson
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6.
Statistics
If X  N (0, 1) and Y 
x/
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Sampling Distribution
2
(n), the distribution of the variate
y / n follows
a. Cauchy’s distribution
b. Fisher’s t distribution
c. Student’s t distribution
d. none of the above
The degrees of freedom for student’s ‘t’ based on a random sample
of size n is
a. n  1 b. n c. n  2 d. (n  1)/2
The relation between the mean and variance of 2 with n df is
a. mean = 2 variance
b. 2 mean = variance
c. mean = variance
d. none of the above
Chi square distribution curve is
a. negatively skewed
b. symmetrical
c. positively skewed
d. None of the above
Chi square distribution is used to test
a. goodness of fit
b. hypothetical value of population variance
c. both (a) and (b)
d. neither (a) nor (b)
Fisher’s Z is closely related to
a. Helmert X2
b. Snedecor’s F
c. Fisher’s t
d. all the above
F distribution was invented by
a. R.A. Fisher
b. G.W. Snedecor
c. W.Z. Gosset
d. J. Neymann
The range of F - variate is
a.  to + 
b. 0 to 1
c. 0 to  d.  to 0
If X  2 (n1), Y  2 (n2) and if X and Y are independent
X + Y follows
a. Chi square distribution with n df
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b. Student’s t distribution with n1 + n2 df
c. Chi square distribution with n1 + n2 df
d. None of the above
Student’s t curve is symmetric about
a. t = 0 b. t = 
c. t = 1 d. t = n
An estimator is a function of
a. population observations
b. sample observations
c. Mean and variance of population
d. None of the above
Estimate and estimator are
a. synonyms
b. different
c. related to population
d. none of the above
The type of estimates are
a. point estimate
b. interval estimate
c. estimates of confidence region
d. all the above
The estimator x of population mean is
a. an unbiased estimator b. a consistant estimator
c. both (a) and (b)
d. neither (a) nor (b)
Factorasation theorem for sufficiency is known as
a. Rao - Blackwell theorem
b. Cramer Rao theorem
c. Chapman Robins theorem
d. Fisher - Neymman theorem
If the sample mean x is an estimate of population mean , then x
is
a. unbiased and efficient
b. unbiased and inefficient
c. biased and efficient
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Statistics
d. biased and inefficient
Sample standard deviation as an estimate of population standard
deviation is
a. unbiased and efficient
b. unbiased and inefficient
c. biased and efficient
d. biased and inefficient
b. t2 is also consistent estimator for 
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a.
c.
30.
If t is a consistent estimator for  , then
a. t is also a consistent estimator for  2
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Sampling Distribution
c. t2 is also consistent estimator for  2
d. none of the above
Least square theory was propounded by whom and in which year?
a. Gauss in 1809 b. Markov in 1900
c. Fisher in 1920 d. None of these
The credit of inventing the method of moments for estimating
parameters goes to
a. R.A. Fisher
b. J. Neymann
c. Laplace
d. Karl Pearson
The concepts of consistency, efficiency and sufficiency are due to
a. J. Neymann
b. R.A. Fisher
c. C.R. Rao
d. J. Berkson
For an estimator to be consistent, the unbiasedness of the estimator
is
a. necessary
b. sufficient
c. necessary as well as sufficient
d. neither necessary nor sufficient
The maximum likelyhood estimates are necessarily
a. unbiased
b. sufficient
c. most efficient d. unique.
The notion of confidence interval was introduced and developed by
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R.A. Fisher
Karl Pearson
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b. J. Neymann
d. Gauss
The 100(1   )% confidence interval for  of N (,  ) when
 unknown, using a sample of size less than 30 is
a.
x  t /
c.
x  t
s
2
n 1
s
n 1
b. x  t  /
d . x  t
2
s
n
s
n
A random sample of 16 housewives has an average body
weight of 52kg and a standard deviation of 3.6kg. 99%
confidence limits for body weight in general are
a.
(54.66, 49.345)
b . (52.66, 51.34)
c.
55.28, 48.72)
d . none of the above
A confidence interval of confidence coefficient 1   is best
which has
a.
smallest width
b . Vastest width
c.
upper and lower limits equidistant from the parameter
d . one sided confidence interval
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Formula for the confidence interval for the ratio of
variances of the two normal population involves
a.
 2 distribution
b . F distribution
c.
t distribution
d . none of the above
An ‘hypothesis’ means
a. assumption
b. a testable preposition
c. theory
d. supposition
A wrong decision about H 0 leads to
a. One kind of error
b. Two kinds of error
c. Three kinds of error
d. Four kinds of error
The idea of testing of hypothesis was first set forth by
a. R.A. Fisher
b. J. Neymann
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Statistics
c. E.L. Lehman
d. A. Wald
Rejecting H0 when H0 is true is
a. Type I error
b. Standard error
c. Sampling error
d. Type II error
Power of a test is related to
a. Type I error
b. Type II error
c. both (a) and (b)
d. neither (a) nor (b)
Level of significance is also called
a. size of the test
b. size of the critical region
c. producer’s risk
d. all the above
Area of critical region depends on
a. size of type I error
b. size of type II error
c. value of the statistic
d. sample size n
A test which maximises the power of the test for a fixed  is known
as
a. optimum test
b. randomised test
c. Bayes test
d. likelihood ratio test
Neymann Pearson lemma provides
a. an unbiased test
b. a most powerful test
c. an admissible test
d. minimax test
Every test statistic is
a. an estimate
b. a random variable
c. a fixed value
d. None of these
Large sample tests are conventionally meant for a sample size
b. Z > 2.58
c. Z  1.96
d. Z  2.58
To test H0 :   500 against H0 :   500, we use
a. one sided left tailed test
b. one sided right tailed test
c. two-tailed test
48.
d. all the above
Testing H0 :   200 against H0 :   500 leads to
a. left tailed test
b. right tailed test
c. two-tailed test d. none of these
49.
To test an hypothesis about proportions of success in a class, the
usual test is
a. t-test
50.
b. F-test
c. Z-test d. None of these
Standard error of the difference of proportions p1  p 2 in two
classes under the hypothesis H0 : p1  p 2 with usual notations is
a.
 1
1 
p *q*


 n1 n 2 
c. p * q *
1
1 
p*


 n1 n 2 
d.
p1q1 p 2 q2

n1
n2
a. central limit theorem
a. 12.0
c. n  30
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1
1

n1 n 2
b.
A parametric test is performed as a large sample test using
b. n < 30
d. n = 100
b. Techebysheff inequality
c. Weak law of large numbers
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a. Z <  2.58
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It is expected that 50% people of a city are cinema goers. A survy
of 1600 people revealed that 35% people go to cinema. The value of
Z statistic is
a. n = 20
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Sampling Distribution
d. none of these
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For a two failed test with  = 0.05, the best critical region of a Z
test is
c. 12.58
d. 12.0
A normal population has a mean of 0.5 and SD = 6.0. The probability
that the sample mean of 625 items of a sample will be negative is
a. 0.0188
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b. 6.0
b. 0.365
c. 0.4812
d. 0.135
The claimed average life of electric bulbs is 2000 hours with a SD =
250 hours. To make 95% sure that the bulbs should not fall below
the claimed average life by more than 5%, the sample size should be
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Statistics
a. 24
b. 16
a.
2.73
b. 0.97
c. 41
d. none of these
c.
3.30
d. 0.41
Student’s ‘t’ test was invented by
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G.W. Snedcor
b. R.A. Fisher
a.
1 to +1
b.  to  
c.
W.Z. Gosset
d. W.G. Cochran
c.
0 to 
d. 0 to 1
Student’s t-etst is applicable only when
the variate values are independent
the variable is distributed normally
the sample is not large
all the above
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paired
b. correlated
c.
equal in number
d. all the above
 2 -test
b. t-test
c.
F-test
d. Z-test
Range of the variance ratio F is
a.
1 to +1
b.  to  
c.
0 to 
d. 0 to 1
Numerator is less than the denominator
b.
Numerator is greater than the denominator
c.
Numerator is equal to the denominator
d.
None of these
Given the following 8 sample values 4, 3, 3, 0, 3, 3, 4, 4 the
value of student’s t test H0: = 0 is
F-test
b. Z-test
c.
 2 -test
d. t-test
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Statistic  2 to test H 0 :  2   02 based on a sample of size n has
degrees of freedom equal to
a. n1
b. n
c. n+1
d. none of these
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Degrees of freedom for  2 in case of contingency table of order
43 are
a. 12
b. 9
c. 8
d. 6
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When d.f. for  2 are 100 or more,  2 is approximated to
While performing the F-est, observe that in the F ratio whether
a.
a.
Degrees of freedom for statistic  2 in case of 22 contigency
table is
a. 3
b. 4
c. 2
d. 1
Equality of two population variances can be tested by
a.
The hypothesis that popultion variance has a specified value can be
tested by
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Paired ‘t’ test is applicable when the observations in the two samples
are
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Range of t statistic is
a.
a.
b.
c.
d.
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Sampling Distribution
a.
c.
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t-distribution
Z-distribution
b. F-distribution
d. none of these
If all frequencies of classes are the same, the value of  2 is
a.
1
b. 
c.
zero
d. none of these
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Sampling Distribution
The range of statistic 
a. 1 to +1
2
is
b.  to  
0 to 
d. 0 to 1
Contingency table having a zero count is called
a. a complete contingency table
b. an incomplete contingency table
c. abnormal contingency table
d. none of these
If the calculated value of  2 is greater than its degrees of freedom,
then
c.
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a.
null hypothesis be accepted directly
b.
null hypothesis be rejected straight-away
c.
 2 table be consulted to arrive at a decision about the null
hypothesis
d.
all the above
ANSWERS
(1)
(6)
(11)
(16)
(21)
(26)
(31)
(36)
(41)
(46)
(51)
(56)
(61)
(66)
c
c
c
b
a
b
a
b
b
c
d
d
b
c
Prepared by:
(2) d
(7) a
(12) c
(17) a
(22) d
(27) b
(32) a
(37) a
(42) b
(47) a
(52) a
(57) c
(62) c
(67) c
(3)
(8)
(13)
(18)
(23)
(28)
(33)
(38)
(43)
(48)
(53)
(58)
(63)
(68)
b
b
d
d
c
b
a
b
b
c
b
c
d
c
(4)
(9)
(14)
(19)
(24)
(29)
(34)
(39)
(44)
(49)
(54)
(59)
(64)
(69)
a
c
c
c
a
b
b
d
c
c
c
b
a
b
(5)
(10)
(15)
(20)
(25)
(30)
(35)
(40)
(45)
(50)
(55)
(60)
(65)
(70)
c
c
a
d
d
a
b
a
a
a
d
d
d
c
Dr. K.X.Joseph, Director,
Academic Staff College,University of Calicut.
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